Roughness of Interfacial Crack Fronts: Stress-Weighted Percolation in the Damage Zone

We study numerically the roughness exponent ζ of an in-plane fracture front slowly propagating along a heterogeneous interface embedded in an elastic body, using a model based on the evolution of a process zone rather than a fracture line. We find ζ=0.60±0.05. For the first time, simulation results are in close agreement with experimental results. We then show that the roughness exponent is related to the correlation length exponent ν of a stress-weighted percolation problem through ζ=ν/(1+ν). A numerical study of the stress-weighted percolation problem yields ν=1.54 giving ζ=0.61 in close agreement with our numerical results and with experimental observations.